which statement about the following equation is true?\n3x² - 8x + 5 = 5x²\nthe discriminant is less than 0…

which statement about the following equation is true?\n3x² - 8x + 5 = 5x²\nthe discriminant is less than 0, so there are two real roots.\nthe discriminant is greater than 0, so there are two real roots.\nthe discriminant is less than 0, so there are two complex roots.\nthe discriminant is greater than 0, so there are two complex roots.

which statement about the following equation is true?\n3x² - 8x + 5 = 5x²\nthe discriminant is less than 0, so there are two real roots.\nthe discriminant is greater than 0, so there are two real roots.\nthe discriminant is less than 0, so there are two complex roots.\nthe discriminant is greater than 0, so there are two complex roots.

Answer

Explanation:

Step1: Rewrite the equation in standard form

First, rewrite (3x^{2}-8x + 5=5x^{2}) as (ax^{2}+bx + c = 0). Subtract (3x^{2}) from both sides: (0=5x^{2}-3x^{2}+8x - 5), so (2x^{2}+8x - 5=0). Here (a = 2), (b = 8), (c=-5).

Step2: Calculate the discriminant

The discriminant formula is (\Delta=b^{2}-4ac). Substitute (a = 2), (b = 8), (c=-5) into the formula: (\Delta=(8)^{2}-4\times2\times(-5)). [ \begin{align*} \Delta&=64+40\ \Delta&=104 \end{align*} ] Since (\Delta = 104>0), when (\Delta>0), the quadratic equation (ax^{2}+bx + c = 0) has two distinct real roots.

Answer:

The discriminant is greater than 0, so there are two real roots.